The basic idea of our proof to Theorem  is the Bethe ansatz, following the approach of [1]} and [2]}. In Section  we consider the one particle case where the interaction between particles is missing as a warm-up. In Section  the two particle case, the simplest non-trivial case, is analysed explicitly, and in Section  the general case is worked out. The essence of the Bethe ansatz is that the interaction among multiple particles is equivalent to the superposition of two-particle interactions. We use the idea implicitly. At last, we prove Corollary REF  in Section .
